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The central theme of this conference is the representation theory of associative algebras and the wide range of powerful methods that have emerged from its development. We aim to bring together an international group of representation theorists, working with categorical, combinatorial, geometric and homological methods, with a view to exchanging ideas and perspectives. The conference is an integral part of the project "Structures for Quivers, Algebras and Representations" (SQUARE), which arises from the collaboration of researchers at the Universites of Padova, Roma-Sapienza, Torino and Verona and is funded by the program PRIN2022 of MUR - Ministero dell'Università e della Ricerca.